Knowledge that Transforms

We examine a simple bargaining setting where heterogeneous buyers and sellers are repeatedly matched with each other. We begin by characterizing efficiency in such a dynamic setting, and discuss how it differs from efficiency in a centralized static setting. We then study the allocations which can result in equilibrium when the matched buyers and sellers bargain through some extensive game form. We take an implementation approach, characterizing the possible allocation rules which result as the extensive game form is varied. We are particularly concerned with the impact of making trade voluntary: imposing individual rationality on and off the equilibrium path. No buyer or seller consummates an agreement which leaves them worse off than the discounted expected value of their future rematching in the market. Finally, we compare and contrast the efficient allocations with those that could ever arise as the equilibria of some voluntary negotiation procedure.

Test statistics are proposed for testing hypotheses about the parameters of the deterministic trend function of a univariate time series. The tests are valid for general forms of serial correlation in the errors and do not require estimates (parametric or nonparametric) of serial correlation parameters. The tests are valid for stationary and unit root errors. Allowable trend functions include linear polynomials of time that may have structural change. Asymptotic results are applied to a model with a simple linear trend and are used to construct confidence intervals for average GNP growth rates for eight industrialized countries using postwar data.

A probability weighting function w(p) is a prominent feature of several nonexpected utility theories, including prospect theory and rank-dependent models. Empirical estimates indicate that w(p) is regressive with respect to the diagonal (w(p) > p for small p, and w(p)

The authors examine discounted repeated games where players privately observe different signals. A leading example is secret price cutting; a firm cannot directly observe rival firms' price cutting but its own sales can imperfectly indicate what is going on. The characterization of equilibria in this class of games has been an open question. The authors construct equilibria where players voluntarily communicate what they have observed and prove folk theorems. Their results thus provide a theoretical support for the conventional wisdom that communication facilitates collusion.

MILGROM AND SHANNON (1994) clarify the relationship between order-theoretic methods for comparative statics and more traditional differential techniques by developing relationships between the differential Spence-Mirrlees single crossing property and the order-theoretic single crossing property. Both conditions are central for monotone comparative statics analysis in a number of settings. In particular, Milgrom and Shannon show that the order-theoretic single crossing property is necessary and sufficient for the set of optimal choices to be nondecreasing in certain choice problems, and that a strict form of the single crossing property guarantees the stronger conclusion that every selection from the set of maximizers is nondecreasing in such problems. Milgrom and Shannon assert that under appropriate conditions the Spence-Mirrlees condition is equivalent to their single crossing property, and that the strict versions are also equivalent. In this note, however, we give counterexamples which show that their strict single crossing property may hold even though the strict Spence-Mirrlees condition fails. In fact, we show that the strict single crossing property may hold even though the strict Spence-Mirrlees condition holds only on a set of arbitrarily small measure. We also give a correct statement of the relationship between the Spence-Mirrlees condition and the single crossing property. These counterexamples explain the discrepancy between the monotonicity conclusions that Milgrom and Shannon (1994) derive from the strict single crossing property and the strict monotonicity conclusions that Edlin and Shannon (1998) derive from the strict Spence-Mirrlees condition. In Section 3 we also use these counterexamples to illustrate the fact that the strict single crossing property can allow both pooling and separating equilibria while the strict Spence-Mirrlees condition eliminates the possibility of pooling equilibria. The elimination of pooling equilibria in signalling and screening models is more subtle than Edlin and Shannon's (1998) strict monotonicity conclusions because agents need not face a differentiable constraint.

Jae-Young Kim, Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models, Econometrica, Vol. 66, No. 2 (Mar., 1998), pp. 359-380

A simple root n consistent, asymptotically normal semiparametric estimator of the coefficient vector beta in the latent variable specification y = L (beta'x + e) is constructed. The distribution of e is unknown and may be correlated with x or be conditionally heteroscedastic, e.g., x can contain measurement error. The function L can also be unknown. The identification assumption is that e is uncorrelated with instruments u and that the conditional distribution of e given x and u does not depend on one of the regressors, which has some special properties. Extensions to more general latent variable specifications are provided.

This paper examines repeated games in which each player observes a private and imperfect signal on the actions played and in which players are allowed to communicate using public messages. Providing incentives for players to reveal their observations generate revelation constraints which, combined with signal imperfections, may be a source of inefficiencies. However, the author shows that, by delaying the revelation of their observations, players may reduce the cost of deterring deviations. With at least three players, he obtains a Nash threat version of the folk theorem. With two players, the author shows that an efficient outcome can (almost) always be approximated.

The authors provide existence proofs and characterization results for the multidimensional version of the multiproduct monopolist problem of M. Mussa and S, Rosen (1978). These results a are also directly applicable to the multidimensional nonlinear pricing problems studied by R. Wilson (1993) and M. Armstrong (1996). The authors establish that bunching is robust in these multidimensional screening problems, even with very regular distributions of types. They consequently design a new technique, the sweeping procedure, for dealing with bunching in multidimensional contexts. This technique extends the ironing procedure of Mussa and Rosen to several dimensions.